<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2006-03-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000005272</issuerCik>
        <issuerName>AMERICAN INTERNATIONAL GROUP INC</issuerName>
        <issuerTradingSymbol>AIG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001236432</rptOwnerCik>
            <rptOwnerName>MATTHEWS EDWARDS E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>399 PARK AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>17TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2006-03-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1237315</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>328820</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>22900</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18644278</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On March 7, 2006, Mr. Matthews entered into an agreement to transfer 1,237,315 shares of American International Group, Inc. (&quot;AIG&quot;) common stock to the 2006 EEM Volaris Trust.    Pursuant to Rule 16a-8 of the Securities and Exchange Act, Mr. Matthews does not have a pecuniary interest in the shares of AIG common stock transferred to the 2006 EEM Volaris Trust.</footnote>
        <footnote id="F2">Mr. Matthews' wife holds 22,900 shares of AIG common stock.  Mr. Matthews may be deemed to be the beneficial owner of, and to have a pecuniary interest in the shares of AIG common stock held by his wife.  Mr. Matthews disclaims beneficial ownership of, and any pecuniary interest in, the shares of AIG common stock held by his wife.</footnote>
        <footnote id="F3">Mr. Matthews may be deemed to be the beneficial owner of, and to have a pecuniary interest in, the shares of AIG common stock held by the C. V. Starr &amp; Co., Inc. Trust (the &quot;CV Starr Trust&quot;).  Mr. Matthews disclaims beneficial ownership of, and any pecuniary interest in, the shares of AIG common stock held by the CV Starr Trust.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Bertil P-H Lundqvist, Attorney-in-Fact;
/s/ Leif B. King, Attorney-in-Fact for Edward E. Matthews</signatureName>
        <signatureDate>2006-03-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
